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Describing soil hydraulic properties with sums of simple functions

Ross, P.J. and Smettem, K.R.J. (1993) Describing soil hydraulic properties with sums of simple functions. Soil Science Society of America Journal, 57 (1). pp. 26-29.

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Simple functions do not adequately describe the hydraulic properties of many field soils, particularly those with substantial macroporosity. By considering the soil pore-size distribution f(ψ) = ΣNi = 1 ψi fi (ψ) corresponding to the effective saturation S(ψ) = ΣNi = 1 ψi Si(ψ), where ψ is matric pressure head, the ψi are fractions of effective porosity, the Si(ψ) are simple water retention functions in common use, and fi(ψ) = S'i(ψ), we show that the relative hydraulic conductivity according to the Mualem model is Kr(ψ) = Sp[ΣΣNi = 1 ψi gi(ψ)/ΣNi = 1 ψi gi(0)]2, where gi(ψ) = εψ-xψ−1 fi(ψ) dψ and p is a pore interaction index. If the pores of the distributions do not interact, the appropriate relation is K(ψ) = ΣNi = 1 KsiKri(ψ), where Ksi is the saturated conductivity of distribution i and Kri = Sp[gi(ψ)/gi(0)]2. We note that the van Genuchten function S(ψ) = [1 + (−αψ)n]−m with the restriction m = 1 − 1/n leads to an infinite slope K'(ψ) at ψ = 0 unless n ≥ 2, which is unrealistic for field soils if a wide range of matric pressure heads is considered. Hydraulic conductivity near saturation is often expressed as K(ψ) = Ks exp(aψ). We introduce the function S(ψ) = (1 − αψ) exp(αψ), which gives, according to Mualem's model, a conductivity K(ψ) = Ks(1 − αψ)p exp[(p + 2)αψ] that approximates Ks exp(αψ) near saturation if a = 2α and is exactly equal if p = 0. As an example, a function using this model for one pore-size distribution and the van Genuchten model for the other was compared with a function using two van Genuchten distributions. The latter gave a slightly improved fit to water content and conductivity data for an aggregated soil.

Publication Type: Journal Article
Publisher: Soil Society of America
Copyright: © Soil Science Society of America.
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